 Hello everyone. Welcome to NPTEL groundwater hydrology and management course. This is week 4, lecture 3. In this week, we are continuing to see the important components for groundwater hydrology. In the last class, we looked at porosity and how it changes and affects the groundwater movement. We understood that specific yield and specific retention are a function of the porosity depends on the porosity. And also, we looked at how the water can move through the porous space and then draw down due to gravity. And some materials would keep the water along with it, the solid particles would cling on to the water and that would be your specific retention. In today's class, we will look at permeability. What is permeability? We can define it as the measure of soil's ability to allow or permit water to flow through its pores or voids, something like your conductance in electric city. So you have a material and how is the material allowing water to pass through? The material is your soil, rock particles, etc. In hydrology, we call it as the matrix. The matrix is the arrangement of soil, solid, soil and other particles. And through the matrix, how does water flow and how does the matrix allow the water to pass through? And that is called permeability derived from the word permit. If you search permeability, you might find that the word spelling is different in different terms. So you can have both spellings in different books. Moving on, you have loose soil. So let's see how a loose soil will differ from a dense soil. In a loose soil, loose means the solid particles are loosely bound. And there is a lot of space in between. And you could see that water can move through easily through the material. In other words, the solid particles permit the water to move freely. Just by looking at this, you can also note that this property is also a function of the porosity and the function of the material. You could manage the porosity or manage the permeability by contacting or tilling those kind of activities. But just for a soil you can take, you have an intrinsic value or dependent value based on the material. So in a loose soil, water can easily flow and it is called high permeability. In a dense soil where the particles are densely packed, closely packed, the porous space is less. And because of the porous space is less, the permeability is less. So in a dense soil, it is difficult to flow the water due to a low permeability. Let's take a very microscopic view of what is happening. Note that Q has units of velocity, which is length and in dimensions. It is not actually a fluid velocity. You can understand that it is not actually the fluid velocity, even though it's meters per second or centimeters per second. You don't call it a velocity. It is the ability of the material to allow the water, how fast water can pass through. But even though the units are, say, similar to velocity, it is not the actual fluid velocity. Just take this example. And you have Q is the discharge going through a cross section of a block A. This is a macroscopic view. In that, you can say, okay, this is a velocity. So you have Q going in, it has Q coming out. You have a car going on a river on a road. It goes through the road and cross section can be put to see how fast it goes. That is velocity. However, in a fluid material and in solid soil material, your water doesn't take the shortest path. You can see that the path is tortuous or it goes around and round until it finds the easiest way to get through. So why not water go up? Because the solid particles are generally packed, water won't go up. So it might come down. So the understanding here is it is not the straight line that the water will take. It has to maneuver meander and then go which way is least resistant. You can see that behavior in rivers also. You don't see the rivers straight. You see them curving up and down, depending on the resistance to flow. So the water particles would go through the path where it is least resistant and it may not be a straight line. So it is not a linear velocity but average linear velocity. You can average it out, take out the noises or it is the poor velocity because it depends on the poor space. The space in between the material, it is called poor velocity. And it is given as V is equals to Q by N e. Q is the velocity of the, or here we define it as the average linear velocity is V and the poor velocity can be taken as V whereas your Q is your permeability and also N e is your effective porosity which means the fraction of connected pore space in the medium. So you can have pore spaces. Let's draw it here. You can have pores spaces in between the material but are they connected? Is water seeing them as connected through the pore or is it seeing it disconnected? So for example, you might have a pore space here but water doesn't see it connected. How much of it is actually connected is the matter. So you can have like these materials and water cannot pass through. So because of that it has to go through like this and that is a kind of meandering cautious path. So your effective porosity is the fraction of connected pore space in the medium. It is also a function of your soil material and also the management practice. If you till the soil, for example, there will be more connections and that is why you see before irrigation farmers normally till the land. They plow the land and so when they apply water it quickly passes through. If they don't, what happens is water stays on the top. Slowly it infiltrates and leads to groundwater recharge but what happens is if it is on the surface too long it gets evaporated. So the farmer is at loss if they don't use the water carefully. So coming back we are at an E which is effective porosity i.e. the fraction of connected pore space in the medium in the matrix or soil and it is a good function to be noticed which is a property of the soil particle. Then we move on to another very very interesting very important relationship between the permeability or intrinsic permeability is intrinsic to the property of the material. So it is given as k rho g by mu is equals to big k and k is called hydraulic conductivity. It is function of both the matrix and the fluid. So this is the first time we are bringing water into the picture. So far we talked about it is the function of the matrix the solid particles and how they are arranged. But this parameter which is hydraulic conductivity brings in the properties of the fluid the fluid being water here and please understand that there would be any other motion within the ground. It could be oil it could be petrol whatever you want to call it crude oil or soluble salt etc chemicals. So all these would have different velocity different conductivity based on the density and that property is only held by the hydraulic conductivity called k. So how is k defined and how is it related to the permeability k is equal to small k or hydraulic conductivity is equal to the permeability times the fluid density times g which is a gravitational acceleration divided by mu. And you have mu as the fluid viscosity. So all this fluid can be put for water. So we have if you're using water for groundwater understanding groundwater for recharge etc we put the values for water and it becomes the row is water density and mu is fluid water viscosity. So look at it here it is not only the ability of the soil or the solid particles to allow water but also the reaction or the interaction between the solid and the water. So fluid density is very very important thick water cannot pass that easily it has to be fluid enough and the viscosity can actually drag. So if the fluid is highly viscous then your solid particles we tag on to it will and will not allow the fluid to pass through. So here is where you have a fluid viscosity coming into the picture. So now density of water can also change depending on the composition of the water. So if you have a very salty water the density is different compared to a fresh water which is recharged through rainfall and the fresh water when it stays with the rock material long enough many many decades or years you have a salt which is dissolved in the water and the fluid water density and viscosity does change. Okay so now when we rearrange this equation you get k which is intrinsic permeability or just permeability is your hydraulic conductivity by mu. So mu hydraulic conductivity times mu by rho g. So what you have here is just rearranging the terms and you get the units of intrinsic permeability. Okay let's do the units to just check if we are doing it when we look at some examples of values but before that we need to understand all my diagrams till now all the book diagrams also you see one dimensional movement either it is left to right or right to left. Okay like for example pure sand particles are easier for water movement because water passes through easily the pure sand has a high effective porosity which means the porous fraction of pores which are connected is very very high. Okay and if you come to sand clay mixture as you see here you have sand the same sand with clay and other particles inside then what happens is the pore space is there but it is not well connected it is retarding the movement of water which means stopping the movement of water and that is not good for the intrinsic permeability because the effective porosity is very less. So you could see water flowing from here in this screen right to left and in the previous examples we saw water moving from left to right but is it one-dimensional is the question is it just x y plane or can we introduce another plane yes for sure we do need to understand that water actually moves from vertically down and then goes horizontally. So there is three-dimensional movement of water and on the three-dimensionals these properties would change so now we are converting one-dimensional into a three-dimensional problem so water along the z plane or it can go to z x or z y okay so all these planes are important for movement of water you cannot restrict it just to one-dimensional it is a three-dimensional movement. So and the process and the forces acting on these would also change so for example if water is moving in the previous way left to right which is after it reaches the activity of gravity doesn't affect your intrinsic permeability nor your hydraulic conductivity so the gravity is there but it doesn't readily pull more however when you have it vertically moving okay you cannot neglect the gravitation force because that is what is pulling the water and in this case what happens is the water is actually stored in the saturation level through gravity. Through gravity there's more water coming in so when more water comes in it has to dissipate it has to move laterally so gravity also plays here indirectly but more force would directly act on the vertical structure. So let's look at the values and the units for hydraulic conductivity it is units of velocity which is given as meters per second whereas your permeability it is a centimeter square or it is called Darcy so Darcy invented these terms so he has his name associated with it we will look at Darcy's experiment in the coming lecture so Darcy is given after his name the unit so Darcy is equal to centimeter square times 10 power 2 okay so you can see just a magnitude all of order difference here so the small k is permeability and the big k is hydraulic conductivity so please note that we need to understand the hydraulic conductivity properties in detail in the coming class but we'll look at permeability and how it shifts so this values I've taken from freeze and cherry which is a book on groundwater the authors are freeze and cherry and they are very very well known across the globe for groundwater work and this book is kind of used like the rule book in many many groundwater research institutes and the data they have has been highly validated so I'm using the same thing here here on your left hand side what you see is the type of the rock or the deposit for soil so this is more your soil type and whereas here it is more of a rock type because groundwater can go in and go into the soil structure and can also come down deep into the groundwater deeper aquifers where you have more rocks so groundwater equations can be used as per the depth change so let's look at a particular value at how to use this conceptual data so you have all these different rock and soil properties what you see is a range if you understand previously even for porosity we did not give you one value we gave a range of values same way here you have a range which starts from let's say silt okay let's say silty sand it starts from this point to this point so all this throughout this is silty sand so first you have to understand what is your rock material or your soil type go to the soil type okay and then you can look at the range let's look at the range of permeability here it is a centimeter square okay so from 10 power minus 10 centimeter square to 10 power minus 6 is the range okay 10 power minus 4 orders of magnitude difference so you can pick anywhere you want I normally pick the center value because kind of averaging out the other values and like this you could apply it to different different data so since k which is your hydraulic conductivity is a function of your permeability where the other terms are just your mu and viscosity the density and also your acceleration due to gravity all are constants for water you could quickly do the calculations to get at k and that is what this graph does it so 10 power minus 9 let's say is kind of the average I wanted to take centimeter square and that equals to approximately 10 power minus 4 centimeters per second or 10 power minus 6 meters per second or another unit's 10 gallons per day per feet square so you can see there is a volume of water moving through a cross section and if you take off the area of the cross section it is purely a velocity kind of a relation let's take a centimeter square so the permeability is 10 power minus 9 for silty sand not very slow but not fast either and you could see that fast when you want to look at the word fast for groundwater movement you could look at hydraulic conductivity which is your k because it is almost in length per unit time and when you see centimeter per second what do you see is water takes that long to pass through a silty sand okay if it is very very you know fast medium let's say gravel you can have it as 10 centimeters per second so think about water and a gravel bed if you pour water water will move through the medium through the gravel bed at 10 meters per second if you want to apply this to a real life scenario let's take the cricket pitch and if you see a rain is coming they quickly run and cover the pitch but before that the rain has already started and water has come on the field but as soon as they take the cover you see that the rain is not much affecting the pitch or the grass why is because they have under the pitch and under the grass a very very highly hydraulic conductive soil it could be a mishop gravel and sand and silt where water when it goes it just flushes through okay so quickly you lose the water which means quickly you keep the system dry in other other sport you see this is golf courses are made like this and that is why it's very expensive these sports to maintain the greenery and also the water budget so when we see water applying to cricket pitches it's a lot of water because it has to first give water to the grass but also it flushes very fast in the system these are the same concepts that you would use when you are constructing a vertical farming or a farm on the rooftop because soil is there you apply water as to go through but excess water has to rush out through the system otherwise water will clog and leak into your building so you have to understand the hydraulic conductivity of the soil and how fast water can move whereas permeability is the how much the material can allow the water to pass through okay so you have different materials here and I would assume all the materials in the world are represented by these simplified versions you can either find it as a silt sand or you can either find it as a rock let's do a quick comparison so silty sand can also correspond to a metamorphic rock or fractured igneous rock okay it can also be part of a permeable basalt so the basalt is what is present in most of India along with your fractured rocks when you call hard rock aquifers and this is what the rock is present so the silty sand values also correspond to your permeable basalt and fractured igneous metamorphic rocks so if you're using a groundwater model the first thing is it will ask is it water the second thing is is it a what is the soil property what is the soil type of soil and what is the hydraulic conductivity so even though there is a range if you don't give the range it will get the average value so be careful about using hydraulic conductivity values in your model so let's look at hydraulic conductivity in detail we can rearrange the equation to give the previous equation to have k which has dimensions of meters per second or length per time and it actually is equal to k is equal to minus q by adh by dl what is dh and dl we will look at it in the following slide so basically the equation is a measure of the fluid initially it was measure of permeability was measure of and how easy it allows but here we're going to do it as a fluid example water and how it can pass through a porous medium so the image is the same because in the previous discussion we looked at the brown particles now we look at water so loose soil easy to flow high permeability high flow high hydraulic conductivity same way you have dense soil low permeability low porosity low hydraulic conductivity so conductivity is a function first of the fluid property and also the soil property it has a minus sign for a reason we will discuss that how it looks by looking through the equation of hydraulic conductivity and the experimental setup as done by Darcy himself in the following lectures for before that we'll finish the microscopic and macroscopic view so what is a macroscopic view is a solid view okay it is combining all these small particles into one unit that is a tube you're not looking at soil individually as soil particles but you're looking at soil as a tube and in the tube by passing water q discharge goes into a cross section a at a average linear velocity v meters per second and it comes out however if you take the macroscopic view out and put the soil in a for example microscope to look at the microscopic view you would see water slowly going through and not straight in a macroscopic view you cannot see the water movement you assume that water is going straight okay but in a microscopic view you can actually see that it is not going straight but in a tortuous way or meandering way and it is variable velocities here the velocity on the top of the tube is the same as the velocity at the bottom of the tube whereas here you have a velocity moving up velocity moving in the in the middle section and on the end sections at different velocities this is the key understanding between the macroscopic which is also the Darcian view and the microscopic approach okay Darci found experimentally that the discharge q is proportional to the difference the height of the water hydraulic head between the ends and inversely proportional to the flow length okay which is L between the length and we will look into detail on how this experiment was set up along with how this equation was arrived in the following I would like to stop today's lecture thank you